Translator Disclaimer
2017 On the reduction modulo $p$ of Mahler equations
Julien Roques
Tohoku Math. J. (2) 69(1): 55-65 (2017). DOI: 10.2748/tmj/1493172128

Abstract

The guiding thread of the present work is the following result, in the vain of Grothendieck's conjecture for differential equations : if the reduction modulo almost all prime $p$ of a given linear Mahler equation with coefficients in $\mathbb{Q}(z)$ has a full set of algebraic solutions, then this equation has a full set of rational solutions. The proof of this result, given at the very end of the paper, relies on intermediate results of independent interest about Mahler equations in characteristic zero as well as in positive characteristic.

Citation

Download Citation

Julien Roques. "On the reduction modulo $p$ of Mahler equations." Tohoku Math. J. (2) 69 (1) 55 - 65, 2017. https://doi.org/10.2748/tmj/1493172128

Information

Published: 2017
First available in Project Euclid: 26 April 2017

zbMATH: 1375.39003
MathSciNet: MR3640014
Digital Object Identifier: 10.2748/tmj/1493172128

Subjects:
Primary: 39A06
Secondary: 12H10, 65Q20

Keywords: Mahler equations

Rights: Copyright © 2017 Tohoku University

JOURNAL ARTICLE
11 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.69 • No. 1 • 2017
Back to Top